text: So per @LowlyDBA's suggestion I decided to test this for myself (to a degree).
  I was actually in the middle of debugging a hot production issue so couldn't really stop to write out the code for a test case. But the code I'm debugging is this scenario. So I made my update to the procedure and looked at the running queries and saw the query text changed from before and after my change to the procedure as the cursor continued to iterate.